The MDL principle states that the best hypothesis (a model and its parameters) for a given set of data is the one that leads to the best compression of the data, namely the minimum codelength [1]}. Specifically, we consider each dimensionality corresponding to a probability model class \(\mathcal {M}_d\) .
\(\mathcal {M}_d= \lbrace  P\left(\mathcal {D};\theta \right):\ \theta = (E\in R^{\left(S_W\times d\right)},\ F\in R^{\left(d \times S_C\right)} ) \rbrace ,\) 
